Each vs. Both

Each and Both Definitions
Each
Being one of two or more considered individually; every
Each person cast a vote. My technique improved with each lesson.
Both
One and the other; relating to or being two in conjunction
Both guests have arrived. Both the books are torn. Both her fingers are broken.
Each
For or to each one; apiece
Ten cents each.
Both
Used with and to indicate that each of two things in a coordinated phrase or clause is included
Both men and women.
An attorney well regarded for both intelligence and honesty.
Each
All; every; qualifying a singular noun, indicating all examples of the thing so named seen as individual or separate items (compare every).
Make sure you wash each bowl well.
The sun comes up each morning and sets each night.
Both
Each of the two; one and the other; referring to two individuals or items.
Both children are such dolls.
Which one do you need? – I need both of them.
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Each
For one; apiece; per.
The apples cost 50 cents each.
Both
Each of the two, or of the two kinds.
"Did you want this one or that one?" — "Give me both."
They were both here.
Each
Every one/thing individually or one by one.
I'm going to give each of you a chance to win.
From each according to his ability, to each according to his needs.
Both
Including both of (used with and).
Both you and I are students.
Each
An individual item: the least quantitative unit in a grouping.
Both
(obsolete) Including all of (used with and).
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Each
Every one of the two or more individuals composing a number of objects, considered separately from the rest. It is used either with or without a following noun; as, each of you or each one of you.
It is a bad thing that men should hate each other; but it is far worse that they should contract the habit of cutting one another's throats without hatred.
Let eachHis adamantine coat gird well.
In each cheek appears a pretty dimple.
Then draw we nearer day by day,Each to his brethren, all to God.
The oak and the elm have each a distinct character.
Both
The one and the other; the two; the pair, without exception of either.
She alone is heir to both of us.
Abraham took sheep and oxen, and gave them unto Abimelech; and both of them made a covenant.
He will not bear the loss of his rank, because he can bear the loss of his estate; but he will bear both, because he is prepared for both.
Thy weal and woe are both of them extremes.
This said, they both betook them several ways.
Each
Every; - sometimes used interchangeably with every.
I know each lane and every alley green.
In short each man's happiness depends upon himself.
Both
As well; not only; equally.
To judge both quick and dead.
A masterpiece both for argument and style.
To whom bothe heven and erthe and see is sene.
Both mongrel, puppy, whelp, and hound.
He prayeth well who loveth wellBoth man and bird and beast.
Each
(used of count nouns) every one considered individually;
Each person is mortal
Each party is welcome
Both
(used with count nouns) two considered together; the two;
Both girls are pretty
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Each
To or from every one of two or more (considered individually);
They received $10 each